Some students planned a picnic. The budget for food was Rs 480. But 8 of them failed to go and thus the cost of food for each member increased by Rs 10. How many students attended the picnic.
Answers
SOLUTION :
Given : Budget for food = ₹ 480
Let the number of students planned a picnic be x .
Share of each student = 480/x
8 students failed to go to picnic , the remaining students = (x - 8)
New share for each student = 480/(x - 8)
480/(x - 8) = 480/x + 10
480/(x - 8) - 480/x = 10
480[1/(x - 8) - 1/x ] = 10
1/(x - 8) - 1/x = 10/480
[x - (x - 8)] / x(x -8) = 1/48
[By taking LCM]
[x - x + 8)] / x² - 8x = 1/48
8/ x² - 8x = 1/48
x² - 8x = 8 × 48
x² - 8x = 384
x² - 8x - 384 = 0
x² + 16x - 24x - 384 = 0
[By middle term splitting]
x(x + 16) - 24(x + 16) = 0
(x - 24)(x + 16) = 0
(x - 24) = 0 or (x + 16) = 0
x = 24 or x = - 16
Since, number of students can't be negative, so x ≠ - 16
Therefore , x = 24
The number of students planned a picnic be 24.
Number of students attended the picnic = (x - 8) = 24 - 8 = 16
Hence, the number of students attended the picnic be 16 .
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